# Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models

arXiv: https://arxiv.org/abs/2305.06704 · HTML: https://mlsanity.com/paper/2305.06704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 78 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 16 of 16)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Enhancing Time Series Momentum Strategies Using Deep Neural Networks](https://mlsanity.com/paper/1904.04912/) (2019)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [SPONGE: A generalized eigenproblem for clustering signed networks](https://mlsanity.com/paper/1904.08575/) (2019)
- [Trading with the Momentum Transformer: An Intelligent and Interpretable Architecture](https://mlsanity.com/paper/2112.08534/) (2021)
- [Sync-Rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and Semidefinite Programming Synchronization](https://mlsanity.com/paper/1504.01070/) (2015)
- [GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks](https://mlsanity.com/paper/2202.00211/) (2022)
- [Slow Momentum with Fast Reversion: A Trading Strategy Using Deep Learning and Changepoint Detection](https://mlsanity.com/paper/2105.13727/) (2021)
- [Lead-lag detection and network clustering for multivariate time series with an application to the US equity market](https://mlsanity.com/paper/2201.08283/) (2022)
- [Multireference Alignment using Semidefinite Programming](https://mlsanity.com/paper/1308.5256/) (2013)
- [Spectral Ranking using Seriation](https://mlsanity.com/paper/1406.5370/) (2014)
- [Ranking and synchronization from pairwise measurements via SVD](https://mlsanity.com/paper/1906.02746/) (2019)
- [Spatio-Temporal Momentum: Jointly Learning Time-Series and Cross-Sectional Strategies](https://mlsanity.com/paper/2302.10175/) (2023)
- [Forecasting COVID-19 Caseloads Using Unsupervised Embedding Clusters of Social Media Posts](https://mlsanity.com/paper/2205.10408/) (2022)
- [State-domain Change Point Detection for Nonlinear Time Series Regression](https://mlsanity.com/paper/1904.11075/) (2019)
- [Transfer Ranking in Finance: Applications to Cross-Sectional Momentum with Data Scarcity](https://mlsanity.com/paper/2208.09968/) (2022)

## Built on by (most cited first, 1 of 1)

- [Few-Shot Learning Patterns in Financial Time-Series for Trend-Following Strategies](https://mlsanity.com/paper/2310.10500/) (2023)

## Abstract (arXiv)

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.